by
Albert Einstein
Lecture at King's College, London, 1921. Published in Mein Weltbild, Amsterdam: Querido Verlag, 1934.

Turning to the theory of relativity itself, I am anxious to draw
attention to the fact that this theory is not speculative in
origin; it owes its invention entirely to the desire to make physical theory fit observed fact as well as possible. We have
here no revolutionary act but the natural continuation of a line
that can be traced through centuries. The abandonment of certain
notions connected with space, time, and motion hitherto treated as
fundamentals must not be regarded as arbitrary, but only as
conditioned by observed facts.

The law of the constant velocity of light in empty space, which
has been confirmed by the development of electrodynamics and
optics, and the equal legitimacy of all inertial systems (special
principle of relativity), which was proved in a particularly
incisive manner by Michelson's famous experiment, between them
made it necessary, to begin with, that the concept of time should
be made relative, each inertial system being given its own special
time.

As this notion was developed, it
became clear that the connection between immediate experience on one side and coordinates and time on the other had hitherto not
been thought out with sufficient precision. It is in general one
of the essential features of the theory of relativity that it is
at pains to work out the relations between general concepts and
empirical facts more precisely. The fundamental principle here is
that the justification for a physical concept lies exclusively in
its clear and unambiguous relation to facts that can be
experienced.

According to the special theory of relativity,
spatial coordinates and time still have an absolute character in
so far as they are directly measurable by stationary clocks and
bodies. But they are relative in so far as they depend on the
state of motion of the selected inertial system. According to the
special theory of relativity the fourdimensional continuum
formed by the union of space and time (Minkowski) retains the
absolute character which, according to the earlier theory,
belonged to both space and time separately. The influence of
motion (relative to the coordinate system) on the form of bodies
and on the motion of clocks, also the equivalence of energy and
inert mass, follow from the interpretation of coordinates and
time as products of measurement.

The general theory of relativity owes its existence in the first
place to the empirical fact of the numerical equality of the
inertial and gravitational mass of bodies, for which fundamental
fact classical mechanics provided no interpretation. Such an interpretation is arrived at by an extension of the principle of
relativity to coordinate systems accelerated relatively to one
another. The introduction of coordinate systems accelerated
relatively to inertial systems involves the appearance of
gravitational fields relative to the latter. As a result of this,
the general theory of relativity, which is based on the equality
of inertia and weight, provides a theory of the gravitational
field.

The introduction of coordinate systems accelerated relatively to
each other as equally legitimate systems, such as they appear
conditioned by the identity of inertia and weight, leads, in con
junction with the results of the special theory of relativity, to
the conclusion that the laws governing the arrangement of solid
bodies in space, when gravitational fields are present, do not
correspond to the laws of Euclidean geometry. An analogous result
follows for the motion of clocks. This brings us to the necessity
for yet another generalization of the theory of space and time,
because the direct interpretation of spatial and temporal
coordinates by means of measurements obtainable with measuring
rods and clocks now breaks down. . That generalization of metric,
which had already been accomplished in the sphere of pure
mathematics through the researches of Gauss and Riemann, is
essentially based on the fact that the metric of the special
theory of relativity can still claim validity for small regions in
the general case as well.

The process of development here sketched strips the spacetime coordinates of all independent reality. The metrically real is now only given through the combination of the spacetime coordinates with the mathematical quantities which describe the
gravitational field.

There is yet another factor underlying the evolution of the
general theory of relativity. As Ernst Mach insistently pointed
out, the Newtonian theory is unsatisfactory in the following
respect: if one considers motion from the purely descriptive, not
from the causal, point of view, it only exists as relative motion
of things with respect to one another. But the acceleration which
figures in Newton's equations of motion is unintelligible if one
starts with the concept of relative motion. It compelled Newton to
invent a physical space in relation to which acceleration was
supposed to exist. This introduction ad hoc of the concept of
absolute space, while logically unexceptionable, nevertheless
seems unsatisfactory. Hence Mach's attempt to alter the mechanical
equations in such a way that the inertia of bodies is traced back
to relative motion on their part not as against absolute space but
as against the totality of other ponderable bodies. In the state
of knowledge then existing, his attempt was bound to fail.

The posing of the problem seems, however, entirely reasonable.
This line of argument imposes itself with considerably enhanced
force in relation to the general theory of relativity,
since, according to that theory, the physical properties of space
are affected by ponderable matter. In my opinion the general
theory of relativity can solve this problem satisfactorily only if
it regards the world as spatially closed. The mathematical results
of the theory force one to this view, if one believes that the
mean density of ponderable matter in the world possesses some
finite value, however small.
